Hilbert modular form data - 2.2.209.1-9.1-g

Formats: - HTML - YAML - JSON - 2024-05-21T05:15:33.623089

• hmf_forms •

  Column	Type
  deg	smallint
  dimension	integer
  disc	bigint
  field_bad_primes	integer[]
  field_label	text
  is_CM	text
  is_base_change	text
  label	text
  label_nsuffix	smallint
  label_suffix	text
  level_bad_primes	integer[]
  level_ideal	text
  level_label	text
  level_norm	integer
  parallel_weight	smallint
  short_label	text
  weight	text

  
  {'deg': 2, 'dimension': 28, 'disc': 209, 'field_bad_primes': [11, 19], 'field_label': '2.2.209.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.209.1-9.1-g', 'label_nsuffix': 6, 'label_suffix': 'g', 'level_bad_primes': [3], 'level_ideal': '[9, 3, 3]', 'level_label': '9.1', 'level_norm': 9, 'parallel_weight': 2, 'short_label': '9.1-g', 'weight': '[2, 2]'}
• hmf_hecke •

  Column	Type
  AL_eigenvalues	jsonb
  hecke_eigenvalues	jsonb
  hecke_polynomial	text
  label	text

  
  {'AL_eigenvalues': [['[9, 3, 3]', -1]], 'hecke_eigenvalues': ['-1951231495281/61159620177776*e^27 + 40672129420383/30579810088888*e^25 - 740645375033633/30579810088888*e^23 + 7753275960888465/30579810088888*e^21 - 103337022709331441/61159620177776*e^19 + 57314182923761655/7644952522222*e^17 - 1375516326985343429/61159620177776*e^15 + 1386032975733393173/30579810088888*e^13 - 455574542168511581/7644952522222*e^11 + 734141313707508723/15289905044444*e^9 - 159474058301303221/7644952522222*e^7 + 13618444794807024/3822476261111*e^5 - 153421011968243/7644952522222*e^3 - 79104955066442/3822476261111*e', 'e', '81322064189/15289905044444*e^26 - 3595292364401/15289905044444*e^24 + 34982731033077/7644952522222*e^22 - 394608232672463/7644952522222*e^20 + 5717531986960135/15289905044444*e^18 - 27836101188724031/15289905044444*e^16 + 92522880412030341/15289905044444*e^14 - 208736813911488855/15289905044444*e^12 + 155402634752479593/7644952522222*e^10 - 71989606893403959/3822476261111*e^8 + 37033665104961033/3822476261111*e^6 - 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7963789261356019/30579810088888*e^23 + 83338844947766401/30579810088888*e^21 - 1110672109767370107/61159620177776*e^19 + 2465371764298125311/30579810088888*e^17 - 14819494450818742623/61159620177776*e^15 + 7502360514647699747/15289905044444*e^13 - 2494852625661851087/3822476261111*e^11 + 8277917845115780503/15289905044444*e^9 - 1949979861634705335/7644952522222*e^7 + 223048082317855473/3822476261111*e^5 - 44816631192698503/7644952522222*e^3 + 916408998210646/3822476261111*e', '80882204534593/61159620177776*e^27 - 847822203473061/15289905044444*e^25 + 31100185013502805/30579810088888*e^23 - 328529057507941451/30579810088888*e^21 + 4429836313956451341/61159620177776*e^19 - 9977763316465315259/30579810088888*e^17 + 61090836656166086985/61159620177776*e^15 - 15828020563815694237/7644952522222*e^13 + 10842844969397232909/3822476261111*e^11 - 37343236241851077141/15289905044444*e^9 + 9202934195937057237/7644952522222*e^7 - 1097920727785367336/3822476261111*e^5 + 207351661269983555/7644952522222*e^3 - 2457036458198760/3822476261111*e', '-6364693038155/15289905044444*e^26 + 265251361844847/15289905044444*e^24 - 2414828770249231/7644952522222*e^22 + 12642510629898214/3822476261111*e^20 - 337300304837122557/15289905044444*e^18 + 1499643950674348865/15289905044444*e^16 - 4516945234522229249/15289905044444*e^14 + 9172746683282309955/15289905044444*e^12 - 3059427464559926008/3822476261111*e^10 + 2539517123179971316/3822476261111*e^8 - 1182912488979640846/3822476261111*e^6 + 253006921522411132/3822476261111*e^4 - 18317294358356594/3822476261111*e^2 + 123172365651888/3822476261111'], 'hecke_polynomial': 'x^28 - 42*x^26 + 772*x^24 - 8178*x^22 + 55341*x^20 - 250568*x^18 + 772599*x^16 - 1618530*x^14 + 2255274*x^12 - 1999412*x^10 + 1043384*x^8 - 283472*x^6 + 36040*x^4 - 1792*x^2 + 16', 'label': '2.2.209.1-9.1-g'}
• hmf_fields •

  Column	Type
  degree	smallint
  discriminant	bigint
  ideals	jsonb
  label	text
  narrow_class_no	smallint
  primes	jsonb

  
  {'degree': 2, 'discriminant': 209, 'ideals': ['[1, 1, 1]', '[2, 2, -11*w - 74]', '[2, 2, -11*w + 85]', '[4, 2, 2]', '[4, 4, -w + 8]', '[4, 4, w + 7]', '[5, 5, 4*w - 31]', '[5, 5, -4*w - 27]', '[8, 4, -22*w - 148]', '[8, 4, -22*w + 170]', '[8, 8, -3*w + 23]', '[8, 8, -3*w - 20]', '[9, 3, 3]', '[10, 10, 7*w + 47]', '[10, 10, w - 7]', '[10, 10, w + 6]', '[10, 10, 7*w - 54]', '[11, 11, -70*w - 471]', '[13, 13, -2*w - 13]', '[13, 13, -2*w + 15]', '[16, 4, 4]', '[16, 8, -2*w + 16]', '[16, 8, 2*w + 14]', '[16, 16, -15*w + 116]', '[16, 16, 15*w + 101]', '[18, 6, -33*w - 222]', '[18, 6, -33*w + 255]', '[19, 19, 92*w - 711]', '[20, 10, 8*w - 62]', '[20, 10, -8*w - 54]', '[20, 20, -59*w - 397]', '[20, 20, -w - 8]', '[20, 20, w - 9]', '[20, 20, 59*w - 456]', '[22, 22, w + 5]', '[22, 22, w - 6]', '[23, 23, -26*w + 201]', '[23, 23, -26*w - 175]', '[25, 5, 5]', '[25, 25, 48*w + 323]', '[25, 25, -48*w + 371]', '[26, 26, -37*w + 286]', '[26, 26, 5*w + 34]', '[26, 26, -5*w + 39]', '[26, 26, 37*w + 249]', '[29, 29, 18*w - 139]', '[29, 29, 18*w + 121]', '[32, 8, -44*w - 296]', '[32, 8, -44*w + 340]', '[32, 16, -6*w + 46]', '[32, 16, -6*w - 40]', '[32, 32, -w - 4]', '[32, 32, -w + 5]', '[36, 6, 6]', '[36, 12, -3*w + 24]', '[36, 12, 3*w + 21]', '[38, 38, -w - 9]', '[38, 38, w - 10]', '[40, 20, 14*w + 94]', '[40, 20, 2*w - 14]', '[40, 20, 2*w + 12]', '[40, 20, 14*w - 108]', '[40, 40, w + 3]', '[40, 40, 103*w + 693]', '[40, 40, 103*w - 796]', '[40, 40, w - 4]', '[41, 41, -10*w - 67]', '[41, 41, 10*w - 77]', '[44, 22, -140*w - 942]', '[44, 44, -19*w - 128]', '[44, 44, 19*w - 147]', '[45, 15, 12*w - 93]', '[45, 15, -12*w - 81]', '[46, 46, -w - 2]', '[46, 46, 5*w - 38]', '[46, 46, -5*w - 33]', '[46, 46, w - 3]', '[47, 47, 2*w - 17]', '[47, 47, 2*w + 15]', '[49, 7, -7]', '[50, 10, -55*w - 370]', '[50, 10, -55*w + 425]', '[50, 50, -w - 1]', '[50, 50, -3*w - 19]', '[50, 50, -3*w + 22]', '[50, 50, -w + 2]', '[52, 26, -4*w - 26]', '[52, 26, -4*w + 30]', '[52, 52, -w]', '[52, 52, -29*w + 224]', '[52, 52, -29*w - 195]', '[52, 52, -w + 1]', '[55, 55, 6*w + 41]', '[55, 55, -6*w + 47]', '[58, 58, -w - 10]', '[58, 58, 9*w - 70]', '[58, 58, -9*w - 61]', '[58, 58, w - 11]', '[64, 8, 8]', '[64, 16, -4*w + 32]', '[64, 16, 4*w + 28]', '[64, 32, -30*w + 232]', '[64, 32, 30*w + 202]', '[64, 64, -129*w + 997]', '[64, 64, 129*w + 868]', '[65, 65, 114*w + 767]', '[65, 65, 2*w - 13]', '[65, 65, 2*w + 11]', '[65, 65, 114*w - 881]', '[72, 12, -66*w - 444]', '[72, 12, -66*w + 510]', '[72, 24, -9*w + 69]', '[72, 24, -9*w - 60]', '[76, 38, 184*w - 1422]', '[76, 76, 25*w + 168]', '[76, 76, 25*w - 193]', '[79, 79, 40*w - 309]', '[79, 79, 40*w + 269]', '[80, 20, 16*w - 124]', '[80, 20, -16*w - 108]', '[80, 40, -118*w - 794]', '[80, 40, -2*w - 16]', '[80, 40, 2*w - 18]', '[80, 40, 118*w - 912]', '[80, 80, -w - 11]', '[80, 80, -41*w - 276]', '[80, 80, 41*w - 317]', '[80, 80, w - 12]', '[81, 9, 9]', '[82, 82, -3*w + 25]', '[82, 82, -23*w - 155]', '[82, 82, -23*w + 178]', '[82, 82, -3*w - 22]', '[88, 44, 2*w + 10]', '[88, 44, 2*w - 12]', '[88, 88, 13*w + 87]', '[88, 88, 13*w - 100]', '[90, 30, 21*w + 141]', '[90, 30, 3*w - 21]', '[90, 30, 3*w + 18]', '[90, 30, 21*w - 162]', '[92, 46, -52*w + 402]', '[92, 46, -52*w - 350]', '[92, 92, -7*w - 48]', '[92, 92, 107*w - 827]', '[92, 92, 107*w + 720]', '[92, 92, -7*w + 55]', '[94, 94, 335*w - 2589]', '[94, 94, -17*w + 131]', '[94, 94, 17*w + 114]', '[94, 94, -125*w + 966]', '[95, 95, -8*w + 61]', '[95, 95, -8*w - 53]', '[98, 14, 77*w + 518]', '[98, 14, 77*w - 595]', '[99, 33, -210*w - 1413]', '[100, 10, 10]', '[100, 20, -5*w + 40]', '[100, 20, 5*w + 35]', '[100, 50, 96*w + 646]', '[100, 50, -96*w + 742]', '[100, 100, -13*w + 101]', '[100, 100, 63*w + 424]', '[100, 100, -63*w + 487]', '[100, 100, 13*w + 88]', '[104, 52, -74*w + 572]', '[104, 52, 10*w + 68]', '[104, 52, -10*w + 78]', '[104, 52, 74*w + 498]', '[104, 104, w + 12]', '[104, 104, -85*w + 657]', '[104, 104, 85*w + 572]', '[104, 104, -w + 13]', '[107, 107, 4*w + 25]', '[107, 107, -4*w + 29]', '[109, 109, 2*w - 11]', '[109, 109, -2*w - 9]', '[110, 110, -51*w + 394]', '[110, 110, -7*w - 46]', '[110, 110, -7*w + 53]', '[110, 110, -51*w - 343]', '[115, 115, -34*w + 263]', '[115, 115, 2*w - 19]', '[115, 115, 2*w + 17]', '[115, 115, -34*w - 229]', '[116, 58, 36*w - 278]', '[116, 58, 36*w + 242]', '[116, 116, 5*w - 37]', '[116, 116, 195*w - 1507]', '[116, 116, 195*w + 1312]', '[116, 116, 5*w + 32]', '[117, 39, -6*w - 39]', '[117, 39, -6*w + 45]', '[121, 11, 11]', '[125, 25, 20*w - 155]', '[125, 25, -20*w - 135]', '[125, 125, 4*w - 33]', '[125, 125, -4*w - 29]', '[127, 127, 136*w + 915]', '[127, 127, 136*w - 1051]', '[128, 16, -88*w - 592]', '[128, 16, -88*w + 680]', '[128, 32, -12*w + 92]', '[128, 32, -12*w - 80]', '[128, 64, -2*w - 8]', '[128, 64, -2*w + 10]', '[128, 128, -3*w + 20]', '[128, 128, -3*w - 17]', '[130, 130, -w - 13]', '[130, 130, -27*w - 182]', '[130, 130, 199*w - 1538]', '[130, 130, -3*w - 23]', '[130, 130, 3*w - 26]', '[130, 130, -199*w - 1339]', '[130, 130, 27*w - 209]', '[130, 130, w - 14]', '[137, 137, -8*w - 55]', '[137, 137, 8*w - 63]', '[143, 143, 32*w + 215]', '[143, 143, 32*w - 247]', '[144, 12, 12]', '[144, 24, -6*w + 48]', '[144, 24, 6*w + 42]', '[144, 48, -45*w + 348]', '[144, 48, 45*w + 303]', '[145, 145, -62*w + 479]', '[145, 145, -2*w + 9]', '[145, 145, -2*w - 7]', '[145, 145, -62*w - 417]', '[151, 151, -16*w - 107]', '[151, 151, 16*w - 123]', '[152, 76, -2*w - 18]', '[152, 76, 2*w - 20]', '[152, 152, 17*w - 132]', '[152, 152, -17*w - 115]', '[157, 157, 188*w + 1265]', '[157, 157, 188*w - 1453]', '[158, 158, -w - 14]', '[158, 158, 11*w - 86]', '[158, 158, -11*w - 75]', '[158, 158, w - 15]', '[160, 40, 28*w + 188]', '[160, 40, 4*w - 28]', '[160, 40, 4*w + 24]', '[160, 40, 28*w - 216]', '[160, 80, 2*w + 6]', '[160, 80, 206*w + 1386]', '[160, 80, 206*w - 1592]', '[160, 80, 2*w - 8]', '[160, 160, 11*w - 84]', '[160, 160, 47*w + 316]', '[160, 160, 47*w - 363]', '[160, 160, 11*w + 73]', '[162, 18, -99*w - 666]', '[162, 18, -99*w + 765]', '[163, 163, 14*w + 95]', '[163, 163, 14*w - 109]', '[164, 82, -20*w - 134]', '[164, 82, 20*w - 154]', '[164, 164, -147*w - 989]', '[164, 164, -3*w - 16]', '[164, 164, 3*w - 19]', '[164, 164, 147*w - 1136]', '[167, 167, -24*w + 185]', '[167, 167, -24*w - 161]', '[169, 13, 13]', '[169, 169, 56*w + 377]', '[169, 169, -56*w + 433]', '[171, 57, 276*w - 2133]', '[173, 173, 2*w - 7]', '[173, 173, -2*w - 5]', '[176, 44, -280*w - 1884]', '[176, 88, -38*w - 256]', '[176, 88, 38*w - 294]', '[176, 176, 5*w - 41]', '[176, 176, -5*w - 36]', '[180, 30, 24*w - 186]', '[180, 30, -24*w - 162]', '[180, 60, -177*w - 1191]', '[180, 60, -3*w - 24]', '[180, 60, 3*w - 27]', '[180, 60, 177*w - 1368]', '[184, 92, -2*w - 4]', '[184, 92, 10*w - 76]', '[184, 92, -10*w - 66]', '[184, 92, 2*w - 6]', '[184, 184, 73*w - 564]', '[184, 184, 5*w + 31]', '[184, 184, -5*w + 36]', '[184, 184, -73*w - 491]', '[188, 94, 4*w - 34]', '[188, 94, 4*w + 30]', '[188, 188, -w - 15]', '[188, 188, 31*w + 209]', '[188, 188, 31*w - 240]', '[188, 188, -w + 16]', '[190, 190, 9*w + 62]', '[190, 190, -67*w + 518]', '[190, 190, 67*w + 451]', '[190, 190, -9*w + 71]', '[191, 191, 2*w - 21]', '[191, 191, -2*w - 19]', '[193, 193, 2*w - 5]', '[193, 193, -2*w - 3]', '[196, 14, 14]', '[196, 28, 7*w - 56]', '[196, 28, -7*w - 49]', '[198, 66, 3*w + 15]', '[198, 66, 3*w - 18]', '[199, 199, 166*w - 1283]', '[199, 199, 166*w + 1117]', '[200, 20, -110*w - 740]', '[200, 20, -110*w + 850]', '[200, 40, -15*w + 115]', '[200, 40, -15*w - 100]', '[200, 100, -2*w - 2]', '[200, 100, -6*w - 38]', '[200, 100, -6*w + 44]', '[200, 100, -2*w + 4]', '[200, 200, -9*w - 59]', '[200, 200, -43*w + 332]', '[200, 200, -43*w - 289]', '[200, 200, -9*w + 68]', '[205, 205, -158*w - 1063]', '[205, 205, 2*w - 3]', '[205, 205, -2*w - 1]', '[205, 205, 158*w - 1221]', '[207, 69, -78*w + 603]', '[207, 69, -78*w - 525]', '[208, 52, -8*w - 52]', '[208, 52, -8*w + 60]', '[208, 104, -2*w]', '[208, 104, -58*w + 448]', '[208, 104, -58*w - 390]', '[208, 104, -2*w + 2]', '[208, 208, -7*w + 52]', '[208, 208, -217*w + 1677]', '[208, 208, -217*w - 1460]', '[208, 208, -7*w - 45]', '[209, 209, -2*w + 1]', '[211, 211, 4*w - 27]', '[211, 211, -4*w - 23]', '[214, 214, 21*w - 163]', '[214, 214, 155*w + 1043]', '[214, 214, 155*w - 1198]', '[214, 214, 21*w + 142]', '[218, 218, 269*w - 2079]', '[218, 218, -49*w + 379]', '[218, 218, -49*w - 330]', '[218, 218, 269*w + 1810]', '[220, 110, 12*w + 82]', '[220, 110, -12*w + 94]', '[220, 220, w + 16]', '[220, 220, 89*w + 599]', '[220, 220, -89*w + 688]', '[220, 220, -w + 17]', '[225, 15, 15]', '[225, 75, 144*w + 969]', '[225, 75, -144*w + 1113]', '[227, 227, 84*w - 649]', '[227, 227, 84*w + 565]', '[229, 229, -100*w + 773]', '[229, 229, -100*w - 673]', '[230, 230, -19*w - 127]', '[230, 230, 39*w + 262]', '[230, 230, -287*w + 2218]', '[230, 230, 3*w - 17]', '[230, 230, -3*w - 14]', '[230, 230, 287*w + 1931]', '[230, 230, -39*w + 301]', '[230, 230, 19*w - 146]', '[232, 116, -2*w - 20]', '[232, 116, 18*w - 140]', '[232, 116, -18*w - 122]', '[232, 116, 2*w - 22]', '[232, 232, 3*w - 28]', '[232, 232, 133*w - 1028]', '[232, 232, -133*w - 895]', '[232, 232, -3*w - 25]', '[234, 78, -111*w + 858]', '[234, 78, 15*w + 102]', '[234, 78, -15*w + 117]', '[234, 78, 111*w + 747]', '[235, 235, 6*w - 49]', '[235, 235, -122*w - 821]', '[235, 235, -122*w + 943]', '[235, 235, 6*w + 43]', '[241, 241, 14*w - 107]', '[241, 241, -14*w - 93]', '[242, 22, -121*w - 814]', '[242, 22, -121*w + 935]', '[245, 35, -28*w + 217]', '[245, 35, 28*w + 189]', '[247, 247, 42*w - 325]', '[247, 247, -42*w - 283]', '[250, 50, 35*w + 235]', '[250, 50, 5*w - 35]', '[250, 50, 5*w + 30]', '[250, 50, 35*w - 270]', '[250, 250, 169*w + 1137]', '[250, 250, 23*w - 177]', '[250, 250, 23*w + 154]', '[250, 250, 169*w - 1306]', '[251, 251, -10*w - 69]', '[251, 251, 10*w - 79]', '[253, 253, -4*w - 31]', '[253, 253, -4*w + 35]', '[254, 254, -w - 17]', '[254, 254, -5*w - 37]', '[254, 254, 5*w - 42]', '[254, 254, w - 18]', '[256, 16, 16]', '[256, 32, -8*w + 64]', '[256, 32, 8*w + 56]', '[256, 64, -60*w + 464]', '[256, 64, 60*w + 404]', '[256, 128, -258*w + 1994]', '[256, 128, 258*w + 1736]', '[256, 256, 35*w + 236]', '[256, 256, -35*w + 271]', '[260, 130, 228*w + 1534]', '[260, 130, 4*w - 26]', '[260, 130, 4*w + 22]', '[260, 130, 228*w - 1762]', '[260, 260, 31*w - 239]', '[260, 260, 3*w + 13]', '[260, 260, 27*w + 181]', '[260, 260, 69*w + 464]', '[260, 260, 69*w - 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460]', '[9992, 4996, -58*w - 402]', '[9992, 4996, 2*w - 102]', '[9992, 9992, -433*w - 2915]', '[9992, 9992, 43*w - 348]', '[9992, 9992, -43*w - 305]', '[9992, 9992, 433*w - 3348]', '[10000, 100, 100]', '[10000, 200, -50*w + 400]', '[10000, 200, 50*w + 350]', '[10000, 400, -375*w + 2900]', '[10000, 400, 375*w + 2525]', '[10000, 500, 960*w + 6460]', '[10000, 500, -960*w + 7420]', '[10000, 1000, -130*w + 1010]', '[10000, 1000, 630*w + 4240]', '[10000, 1000, -630*w + 4870]', '[10000, 1000, 130*w + 880]', '[10000, 2000, -15*w + 155]', '[10000, 2000, 85*w + 580]', '[10000, 2000, -85*w + 665]', '[10000, 2000, 15*w + 140]', '[10000, 2500, -32*w + 268]', '[10000, 2500, 32*w + 236]', '[10000, 5000, 6*w + 106]', '[10000, 5000, 246*w + 1658]', '[10000, 5000, -246*w + 1904]', '[10000, 5000, -6*w + 112]', '[10000, 10000, -1813*w + 14012]', '[10000, 10000, -77*w + 604]', '[10000, 10000, 77*w + 527]', '[10000, 10000, 1813*w + 12199]'], 'label': '2.2.209.1', 'narrow_class_no': 2, 'primes': ['[2, 2, -11*w - 74]', '[2, 2, -11*w + 85]', '[5, 5, 4*w - 31]', '[5, 5, -4*w - 27]', '[9, 3, 3]', '[11, 11, -70*w - 471]', '[13, 13, -2*w - 13]', '[13, 13, -2*w + 15]', '[19, 19, 92*w - 711]', '[23, 23, -26*w + 201]', '[23, 23, -26*w - 175]', '[29, 29, 18*w - 139]', '[29, 29, 18*w + 121]', '[41, 41, -10*w - 67]', '[41, 41, 10*w - 77]', '[47, 47, 2*w - 17]', '[47, 47, 2*w + 15]', '[49, 7, -7]', '[79, 79, 40*w - 309]', '[79, 79, 40*w + 269]', '[107, 107, 4*w + 25]', '[107, 107, -4*w + 29]', '[109, 109, 2*w - 11]', '[109, 109, -2*w - 9]', '[127, 127, 136*w + 915]', '[127, 127, 136*w - 1051]', '[137, 137, -8*w - 55]', '[137, 137, 8*w - 63]', '[151, 151, -16*w - 107]', '[151, 151, 16*w - 123]', '[157, 157, 188*w + 1265]', '[157, 157, 188*w - 1453]', '[163, 163, 14*w + 95]', '[163, 163, 14*w - 109]', '[167, 167, -24*w + 185]', '[167, 167, -24*w - 161]', '[173, 173, 2*w - 7]', '[173, 173, -2*w - 5]', '[191, 191, 2*w - 21]', '[191, 191, -2*w - 19]', '[193, 193, 2*w - 5]', '[193, 193, -2*w - 3]', '[199, 199, 166*w - 1283]', '[199, 199, 166*w + 1117]', '[211, 211, 4*w - 27]', '[211, 211, -4*w - 23]', '[227, 227, 84*w - 649]', '[227, 227, 84*w + 565]', '[229, 229, -100*w + 773]', '[229, 229, -100*w - 673]', '[241, 241, 14*w - 107]', '[241, 241, -14*w - 93]', '[251, 251, -10*w - 69]', '[251, 251, 10*w - 79]', '[281, 281, 6*w + 37]', '[281, 281, -6*w + 43]', '[289, 17, -17]', '[293, 293, 298*w + 2005]', '[293, 293, 298*w - 2303]', '[307, 307, -4*w - 21]', '[307, 307, 4*w - 25]', '[311, 311, 22*w + 149]', '[311, 311, -22*w + 171]', '[313, 313, 16*w - 125]', '[313, 313, -16*w - 109]', '[337, 337, 46*w + 309]', '[337, 337, -46*w + 355]', '[353, 353, -64*w + 495]', '[353, 353, -64*w - 431]', '[367, 367, 2*w - 25]', '[367, 367, -2*w - 23]', '[373, 373, -38*w + 293]', '[373, 373, 38*w + 255]', '[389, 389, 4*w - 37]', '[389, 389, -4*w - 33]', '[397, 397, -12*w - 83]', '[397, 397, 12*w - 95]', '[409, 409, 202*w + 1359]', '[409, 409, 202*w - 1561]', '[419, 419, -50*w + 387]', '[419, 419, 50*w + 337]', '[431, 431, 320*w - 2473]', '[431, 431, 320*w + 2153]', '[439, 439, 128*w - 989]', '[439, 439, 128*w + 861]', '[443, 443, -86*w - 579]', '[443, 443, -86*w + 665]', '[463, 463, 306*w + 2059]', '[463, 463, 306*w - 2365]', '[467, 467, 2*w - 27]', '[467, 467, -2*w - 25]', '[499, 499, 30*w + 203]', '[499, 499, -30*w + 233]', '[523, 523, 68*w + 457]', '[523, 523, 68*w - 525]', '[547, 547, 4*w - 19]', '[547, 547, -4*w - 15]', '[563, 563, -28*w - 187]', '[563, 563, 28*w - 215]', '[569, 569, 150*w - 1159]', '[569, 569, 150*w + 1009]', '[577, 577, 72*w + 485]', '[577, 577, 72*w - 557]', '[587, 587, 262*w - 2025]', '[587, 587, 262*w + 1763]', '[601, 601, -10*w + 73]', '[601, 601, 10*w + 63]', '[607, 607, 16*w - 121]', '[607, 607, -16*w - 105]', '[617, 617, -152*w + 1175]', '[617, 617, -152*w - 1023]', '[619, 619, -6*w - 47]', '[619, 619, 6*w - 53]', '[631, 631, -58*w + 449]', '[631, 631, 58*w + 391]', '[643, 643, -174*w + 1345]', '[643, 643, -174*w - 1171]', '[647, 647, 218*w + 1467]', '[647, 647, 218*w - 1685]', '[653, 653, -196*w - 1319]', '[653, 653, 196*w - 1515]', '[659, 659, -52*w + 401]', '[659, 659, 52*w + 349]', '[673, 673, 482*w + 3243]', '[673, 673, 482*w - 3725]', '[677, 677, 246*w + 1655]', '[677, 677, 246*w - 1901]', '[691, 691, 2*w - 31]', '[691, 691, -2*w - 29]', '[709, 709, 20*w + 137]', '[709, 709, 20*w - 157]', '[719, 719, -94*w + 727]', '[719, 719, -94*w - 633]', '[727, 727, 38*w + 257]', '[727, 727, -38*w + 295]', '[743, 743, -8*w + 55]', '[743, 743, 8*w + 47]', '[757, 757, 12*w - 97]', '[757, 757, 12*w + 85]', '[787, 787, -4*w - 5]', '[787, 787, 4*w - 9]', '[811, 811, 4*w - 7]', '[811, 811, -4*w - 3]', '[823, 823, 6*w - 55]', '[823, 823, -6*w - 49]', '[827, 827, -4*w - 1]', '[827, 827, 4*w - 5]', '[857, 857, 6*w - 35]', '[857, 857, -6*w - 29]', '[859, 859, -10*w - 73]', '[859, 859, 10*w - 83]', '[877, 877, 194*w - 1499]', '[877, 877, 194*w + 1305]', '[881, 881, -8*w - 61]', '[881, 881, 8*w - 69]', '[883, 883, -66*w + 511]', '[883, 883, 66*w + 445]', '[887, 887, 504*w + 3391]', '[887, 887, 504*w - 3895]', '[929, 929, 424*w + 2853]', '[929, 929, 424*w - 3277]', '[941, 941, 386*w - 2983]', '[941, 941, 386*w + 2597]', '[947, 947, 2*w - 35]', '[947, 947, -2*w - 33]', '[953, 953, 22*w - 167]', '[953, 953, -22*w - 145]', '[961, 31, -31]']}
• nf_fields •

  Column	Type
  class_group	jsonb
  class_number	numeric
  cm	boolean
  coeffs	numeric[]
  conductor	numeric
  degree	smallint
  disc_abs	numeric
  disc_rad	numeric
  disc_sign	smallint
  embeddings_gen_imag	double precision[]
  embeddings_gen_real	double precision[]
  gal_is_abelian	boolean
  gal_is_cyclic	boolean
  gal_is_solvable	boolean
  galois_disc_exponents	numeric[]
  galois_label	text
  galt	integer
  grd	double precision
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  is_minimal_sibling	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  minimal_sibling	numeric[]
  monogenic	smallint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  used_grh	boolean
  dirichlet_group	bigint[]
  frobs	jsonb
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-52, -1, 1], 'conductor': 209, 'degree': 2, 'dirichlet_group': [1, 208], 'disc_abs': 209, 'disc_rad': 209, 'disc_sign': 1, 'frobs': [[2, [[1, 2]]], [3, [[2, 1]]], [5, [[1, 2]]], [7, [[2, 1]]], [11, [0]], [13, [[1, 2]]], [17, [[2, 1]]], [19, [0]], [23, [[1, 2]]], [29, [[1, 2]]], [31, [[2, 1]]], [37, [[2, 1]]], [41, [[1, 2]]], [43, [[2, 1]]], [47, [[1, 2]]], [53, [[2, 1]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 14.45683229480096, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.209.1', 'local_algs': ['11.2.1.2', '19.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [11, 19], 'rd': 14.4568322948, 'regulator': {'__RealLiteral__': 0, 'data': '11.4414509452', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 6440 a + 43331 \\)'], 'used_grh': False, 'zk': ['1', 'a']}